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📖 OVERVIEW
📖 OVERVIEW
My doctoral research addresses the inherent challenges found within stochastic evolution equations. I focus on bridging the gap between abstract theoretical frameworks and practical numerical computation.
Core Areas of Investigation:
Theoretical Analysis: Establishing existence, uniqueness, and spatial-temporal regularity of mild solutions for semilinear SPDEs driven by infinite-dimensional noise (including locally Lipschitz nonlinearities and low-regularity initial data).
Numerical Discretization: Formulating robust numerical methods, specifically utilizing the Finite Element Method (FEM), to simulate complex equations like the stochastic Burgers and Allen-Cahn equations.
📝 MANUSCRIPTS & WORKING PAPERS
📝 MANUSCRIPTS & WORKING PAPERS
Existence, Uniqueness, and Pathwise Regularity for Multidimensional Semilinear SPDEs with Locally Lipschitz Coefficients and Rough Initial Data (Preprint)
A comprehensive study utilizing the semigroup theoretic approach to analyze multidimensional stochastic evolution equations.
Optimal Error Estimates of a Finite Element Method for Semilinear SPDEs with Additive Noise and Nonsmooth Initial Data (Preprint)
Optimal Error Estimates of a Finite Element Method for Semilinear SPDEs with Multiplicative Noise and Rough Initial Data (Manuscript in preparation)
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